TODO

Survival

Forest Fragments

Diagnostics

s_1ha_res <- qresid(s_1ha)
par(mfrow = c(2,2))
#histogram
plot(density(s_1ha_res))
#QQ plot
qqnorm(s_1ha_res); qqline(s_1ha_res)
#Fitted vs. residuals--binned residuals plot
binnedplot(fitted(s_1ha), residuals(s_1ha, type = "response"))

Basis dimensions

pdf(NULL)
gam.check(s_1ha)
## 
## Method: fREML   Optimizer: perf newton
## full convergence after 13 iterations.
## Gradient range [-5.769935e-05,5.853239e-06]
## (score 12515.55 & scale 1).
## Hessian positive definite, eigenvalue range [1.466609e-05,1.038272].
## Model rank =  85 / 85 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                         k'      edf k-index p-value
## s(log_size_prev)  9.00e+00 2.86e+00    0.93    0.34
## s(plot)           4.00e+00 1.27e-04      NA      NA
## s(spei_history,L) 7.00e+01 4.97e+00      NA      NA
dev.off()
## quartz_off_screen 
##                 2

Basis dimension checking with gam.check() doesn’t appear to work for dlnm crossbasis smooths. Instead I’ll use a method described in the help file ?choose.k to check for adequate knots. Unfortunately, bs = "cs" doesn’t work with dlnm, so I’ll use select = TRUE instead to reduce chance of overfitting.

# looking for near zero edf
gam(s_1ha_res ~ s(log_size_prev, k = 10, bs = "cs"), gamma = 1.4,
    data = model.frame(s_1ha)) #fine
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## s_1ha_res ~ s(log_size_prev, k = 10, bs = "cs")
## 
## Estimated degrees of freedom:
## 0.153  total = 1.15 
## 
## GCV score: 0.9861161
gam(s_1ha_res ~ s(spei_history, L,
      bs = "cb",
      k = c(3, 35),
      xt = list(bs = "cr")),
    gamma = 1.4,
    select = TRUE,
    data = model.frame(s_1ha)) #fine
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## s_1ha_res ~ s(spei_history, L, bs = "cb", k = c(3, 35), xt = list(bs = "cr"))
## 
## Estimated degrees of freedom:
## 0  total = 1 
## 
## GCV score: 0.9861201

Summary

summary(s_1ha)
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## surv ~ flwr_prev + s(log_size_prev, bs = "cr") + s(plot, bs = "re") + 
##     s(spei_history, L, bs = "cb", k = c(3, 35), xt = list(bs = "cr"))
## 
## Parametric coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  3.17262    0.07856  40.386   <2e-16 ***
## flwr_prev1  -0.51788    0.44094  -1.174     0.24    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                         edf Ref.df Chi.sq p-value    
## s(log_size_prev)  2.8566448      9 359.56  <2e-16 ***
## s(plot)           0.0001271      3   0.00   0.507    
## s(spei_history,L) 4.9668620     27  57.58  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.0599   Deviance explained = 13.2%
## fREML =  12516  Scale est. = 1         n = 9183
draw(s_1ha)
## Warning: Removed 910 rows containing non-finite values (stat_contour).

Continuous Forest

Diagnostics

s_cf_res <- qresid(s_cf)
par(mfrow = c(2,2))
#histogram
plot(density(s_cf_res))
#QQ plot
qqnorm(s_cf_res); qqline(s_cf_res)
#Fitted vs. residuals--binned residuals plot
binnedplot(fitted(s_cf), residuals(s_cf, type = "response"))

### Basis dimensions

pdf(NULL)
gam.check(s_cf)
## 
## Method: fREML   Optimizer: perf newton
## full convergence after 12 iterations.
## Gradient range [-8.212922e-09,1.675182e-06]
## (score 43592.6 & scale 1).
## Hessian positive definite, eigenvalue range [0.3172497,1.876293].
## Model rank =  87 / 87 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                      k'   edf k-index p-value
## s(log_size_prev)   9.00  3.46    0.96    0.84
## s(plot)            6.00  4.40      NA      NA
## s(spei_history,L) 70.00 11.10      NA      NA
dev.off()
## quartz_off_screen 
##                 2
# looking for near zero edf
gam(s_cf_res ~ s(log_size_prev, k = 10, bs = "cs"), gamma = 1.4,
    data = model.frame(s_cf)) #fine
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## s_cf_res ~ s(log_size_prev, k = 10, bs = "cs")
## 
## Estimated degrees of freedom:
## 0.421  total = 1.42 
## 
## GCV score: 1.003405
gam(s_cf_res ~ s(spei_history, L,
      bs = "cb",
      k = c(3, 35),
      xt = list(bs = "cr")),
    gamma = 1.4,
    select = TRUE,
    data = model.frame(s_cf)) 
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## s_cf_res ~ s(spei_history, L, bs = "cb", k = c(3, 35), xt = list(bs = "cr"))
## 
## Estimated degrees of freedom:
## 13.3  total = 14.26 
## 
## GCV score: 1.003749

Summary

summary(s_cf)
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## surv ~ flwr_prev + s(log_size_prev, bs = "cr") + s(plot, bs = "re") + 
##     s(spei_history, L, bs = "cb", k = c(3, 35), xt = list(bs = "cr"))
## 
## Parametric coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  3.41882    0.14056  24.323   <2e-16 ***
## flwr_prev1   0.09828    0.26873   0.366    0.715    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                      edf Ref.df  Chi.sq p-value    
## s(log_size_prev)   3.455      9 1976.65  <2e-16 ***
## s(plot)            4.404      5   42.83  <2e-16 ***
## s(spei_history,L) 11.101     20  180.47  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.113   Deviance explained =   20%
## fREML =  43593  Scale est. = 1         n = 31701
draw(s_cf)
## Warning: Removed 939 rows containing non-finite values (stat_contour).

Effect of sample size

Here I use a random sub-sample to check that differences between continuous forest and fragments are not purely due to sample size differences, particularly differences in the complexity of the crossbasis smooth.

summary(s_1ha)$edf[3]
## [1] 4.966862
summary(s_cf)$edf[3]
## [1] 11.1015
summary(s_cf_sub)$edf[3]
## [1] 1.930495
draw(s_cf_sub)
## Warning: Removed 910 rows containing non-finite values (stat_contour).

Surface still looks different in a similar way though.

Growth

Fragments

Diagnostics

appraise(g_1ha)

Basis dimensions

pdf(NULL)
gam.check(g_1ha)
## 
## Method: fREML   Optimizer: perf newton
## full convergence after 14 iterations.
## Gradient range [-2.066654e-10,7.391816e-08]
## (score 12196.75 & scale 1).
## Hessian positive definite, eigenvalue range [0.08811498,3.622954].
## Model rank =  85 / 85 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                      k'   edf k-index p-value
## s(log_size_prev)   9.00  4.19       1    0.56
## s(plot)            4.00  2.70      NA      NA
## s(spei_history,L) 70.00 18.39      NA      NA
dev.off()
## quartz_off_screen 
##                 2
g_1ha_res <- residuals(g_1ha)
# looking for near zero edf
gam(g_1ha_res ~ s(log_size_prev, k = 10, bs = "cs"), gamma = 1.4,
    data = model.frame(g_1ha)) #fine
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## g_1ha_res ~ s(log_size_prev, k = 10, bs = "cs")
## 
## Estimated degrees of freedom:
## 1.84  total = 2.84 
## 
## GCV score: 1.331934
gam(g_1ha_res ~ s(spei_history, L,
      bs = "cb",
      k = c(3, 35),
      xt = list(bs = "cr")),
    gamma = 1.4,
    select = TRUE,
    data = model.frame(g_1ha)) #fine
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## g_1ha_res ~ s(spei_history, L, bs = "cb", k = c(3, 35), xt = list(bs = "cr"))
## 
## Estimated degrees of freedom:
## 0.584  total = 1.58 
## 
## GCV score: 1.3363

Summary

summary(g_1ha)
## 
## Family: Scaled t(4.727,0.477) 
## Link function: identity 
## 
## Formula:
## log_size ~ flwr_prev + s(log_size_prev, bs = "cr") + s(plot, 
##     bs = "re") + s(spei_history, L, bs = "cb", k = c(3, 35), 
##     xt = list(bs = "cr"))
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  4.37803    0.10625  41.205   <2e-16 ***
## flwr_prev1   0.08474    0.03600   2.354   0.0186 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                      edf Ref.df       F  p-value    
## s(log_size_prev)   4.186      9 2943.17  < 2e-16 ***
## s(plot)            2.705      3   20.38  < 2e-16 ***
## s(spei_history,L) 18.385     21   23.37 8.05e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.696   Deviance explained = 63.2%
## fREML =  12197  Scale est. = 1         n = 8527
draw(g_1ha)
## Warning: Removed 910 rows containing non-finite values (stat_contour).

Continuous Forest

Diagnostics

gratia::appraise(g_cf)

Basis dimensions

pdf(NULL)
gam.check(g_cf)
## 
## Method: fREML   Optimizer: perf newton
## full convergence after 14 iterations.
## Gradient range [-3.633122e-10,9.547658e-07]
## (score 41017.73 & scale 1).
## Hessian positive definite, eigenvalue range [0.1892746,2.035307].
## Model rank =  87 / 87 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                      k'   edf k-index p-value
## s(log_size_prev)   9.00  5.72    0.98     0.1
## s(plot)            6.00  4.08      NA      NA
## s(spei_history,L) 70.00 13.64      NA      NA
dev.off()
## quartz_off_screen 
##                 2
g_cf_res <- residuals(g_cf)
# looking for near zero edf
gam(g_cf_res ~ s(log_size_prev, k = 10, bs = "cs"), gamma = 1.4,
    data = model.frame(g_cf)) #fine
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## g_cf_res ~ s(log_size_prev, k = 10, bs = "cs")
## 
## Estimated degrees of freedom:
## 2.53  total = 3.53 
## 
## GCV score: 1.406485
gam(g_cf_res ~ s(spei_history, L,
      bs = "cb",
      k = c(3, 35),
      xt = list(bs = "cr")),
    gamma = 1.4,
    select = TRUE,
    data = model.frame(g_cf)) #fine
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## g_cf_res ~ s(spei_history, L, bs = "cb", k = c(3, 35), xt = list(bs = "cr"))
## 
## Estimated degrees of freedom:
## 15  total = 15.97 
## 
## GCV score: 1.412272

Summary

summary(g_cf)
## 
## Family: Scaled t(3.903,0.416) 
## Link function: identity 
## 
## Formula:
## log_size ~ flwr_prev + s(log_size_prev, bs = "cr") + s(plot, 
##     bs = "re") + s(spei_history, L, bs = "cb", k = c(3, 35), 
##     xt = list(bs = "cr"))
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  4.35421    0.02597 167.665   <2e-16 ***
## flwr_prev1   0.02795    0.01482   1.886   0.0594 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                      edf Ref.df         F p-value    
## s(log_size_prev)   5.719      9 17697.579  <2e-16 ***
## s(plot)            4.077      5     6.703  <2e-16 ***
## s(spei_history,L) 13.645     19   101.657  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.784   Deviance explained = 69.1%
## fREML =  41018  Scale est. = 1         n = 28849
draw(g_cf)
## Warning: Removed 968 rows containing non-finite values (stat_contour).

Continuous Forest subsample

To check that differences are not purely due to sample size differences, particularly that lower edf in continuous forests is due to higher sample size.

summary(g_1ha)$edf[3]
## [1] 18.38534
summary(g_cf)$edf[3]
## [1] 13.64452
summary(g_cf_sub)$edf[3]
## [1] 12.33543

edf of subsample is similar to full dataset, despite differences in sample size.

draw(g_cf_sub)
## Warning: Removed 910 rows containing non-finite values (stat_contour).

Crossbasis surface looks nearly identical.

Flowering

Fragments

Diagnostics

f_1ha_res <- qresid(f_1ha)
par(mfrow = c(2,2))
#histogram
plot(density(f_1ha_res))
#QQ plot
qqnorm(f_1ha_res); qqline(f_1ha_res)
#Fitted vs. residuals--binned residuals plot
binnedplot(fitted(f_1ha), residuals(f_1ha, type = "response"))

Basis dimensions

pdf(NULL)
gam.check(f_1ha)
## 
## Method: fREML   Optimizer: perf newton
## full convergence after 18 iterations.
## Gradient range [-6.392746e-09,4.200497e-08]
## (score 10584.82 & scale 1).
## Hessian positive definite, eigenvalue range [0.3677846,6.412113].
## Model rank =  1351 / 1351 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                        k'     edf k-index p-value
## s(log_size_prev)     9.00    3.32    0.99    0.99
## s(plot)              4.00    2.51      NA      NA
## s(spei_history,L)   70.00    9.76      NA      NA
## s(ha_id_number)   1266.00   67.21      NA      NA
dev.off()
## quartz_off_screen 
##                 2
# looking for near zero edf
gam(f_1ha_res ~ s(log_size_prev, k = 10, bs = "cs"), gamma = 1.4,
    data = model.frame(f_1ha)) #fine
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## f_1ha_res ~ s(log_size_prev, k = 10, bs = "cs")
## 
## Estimated degrees of freedom:
## 0  total = 1 
## 
## GCV score: 0.986224
gam(f_1ha_res ~ s(spei_history, L,
      bs = "cb",
      k = c(3, 35),
      xt = list(bs = "cr")),
    gamma = 1.4,
    select = TRUE,
    data = model.frame(f_1ha)) #fine
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## f_1ha_res ~ s(spei_history, L, bs = "cb", k = c(3, 35), xt = list(bs = "cr"))
## 
## Estimated degrees of freedom:
## 0.709  total = 1.71 
## 
## GCV score: 0.9861867

Summary

summary(f_1ha)
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## flwr ~ flwr_prev + s(log_size_prev, bs = "cr") + s(plot, bs = "re") + 
##     s(spei_history, L, bs = "cb", k = c(3, 35), xt = list(bs = "cr")) + 
##     s(ha_id_number, bs = "re")
## 
## Parametric coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  -5.9700     0.5369 -11.119  < 2e-16 ***
## flwr_prev1    0.7084     0.1739   4.075  4.6e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                      edf Ref.df Chi.sq p-value    
## s(log_size_prev)   3.318      9 364.88 < 2e-16 ***
## s(plot)            2.505      3  20.39 0.00108 ** 
## s(spei_history,L)  9.758     21  88.71 < 2e-16 ***
## s(ha_id_number)   67.206   1265  85.76 0.00092 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =   0.29   Deviance explained = 44.5%
## fREML =  10585  Scale est. = 1         n = 8527
draw(f_1ha)
## Warning: Removed 910 rows containing non-finite values (stat_contour).

Continuous Forest

Diagnostics

f_cf_res <- qresid(f_cf)
par(mfrow = c(2,2))
#histogram
plot(density(f_cf_res))
#QQ plot
qqnorm(f_cf_res); qqline(f_cf_res)
#Fitted vs. residuals--binned residuals plot
binnedplot(fitted(f_cf), residuals(f_cf, type = "response"))

Basis dimensions

pdf(NULL)
gam.check(f_cf)
## 
## Method: fREML   Optimizer: perf newton
## full convergence after 10 iterations.
## Gradient range [-2.011692e-05,8.805875e-06]
## (score 36174.51 & scale 1).
## Hessian positive definite, eigenvalue range [2.007401e-05,48.30054].
## Model rank =  4477 / 4477 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                       k'    edf k-index p-value
## s(log_size_prev)     9.0    5.7       1       1
## s(plot)              6.0    3.9      NA      NA
## s(spei_history,L)   70.0   10.3      NA      NA
## s(ha_id_number)   4390.0  351.7      NA      NA
dev.off()
## quartz_off_screen 
##                 2
# looking for near zero edf
gam(f_cf_res ~ s(log_size_prev, k = 10, bs = "cs"), gamma = 1.4,
    data = model.frame(f_cf)) #fine
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## f_cf_res ~ s(log_size_prev, k = 10, bs = "cs")
## 
## Estimated degrees of freedom:
## 0  total = 1 
## 
## GCV score: 0.9989736
gam(f_cf_res ~ s(spei_history, L,
      bs = "cb",
      k = c(3, 35),
      xt = list(bs = "cr")),
    gamma = 1.4,
    select = TRUE,
    data = model.frame(f_cf)) #fine
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## f_cf_res ~ s(spei_history, L, bs = "cb", k = c(3, 35), xt = list(bs = "cr"))
## 
## Estimated degrees of freedom:
## 1.4  total = 2.4 
## 
## GCV score: 0.9988722

Summary

summary(f_cf)
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## flwr ~ flwr_prev + s(log_size_prev, bs = "cr") + s(plot, bs = "re") + 
##     s(spei_history, L, bs = "cb", k = c(3, 35), xt = list(bs = "cr")) + 
##     s(ha_id_number, bs = "re")
## 
## Parametric coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -5.39245    0.24028 -22.442  < 2e-16 ***
## flwr_prev1   0.53988    0.08756   6.166 7.01e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                       edf Ref.df  Chi.sq p-value    
## s(log_size_prev)    5.698      9 2104.21  <2e-16 ***
## s(plot)             3.900      5   69.33  <2e-16 ***
## s(spei_history,L)  10.325     21  425.95  <2e-16 ***
## s(ha_id_number)   351.687   4389  494.24  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.267   Deviance explained = 40.6%
## fREML =  36175  Scale est. = 1         n = 28849
draw(f_cf)
## Warning: Removed 968 rows containing non-finite values (stat_contour).

Continuous Forest subsample

To check that differences are not purely due to sample size differences, particularly that lower edf in continuous forests is due to higher sample size. For flowering, edf is actually slightly higher in CF with a larger sample size. With subsample, edf are more similar.

summary(f_1ha)$edf[3]
## [1] 9.758276
summary(f_cf)$edf[3]
## [1] 10.32503
summary(f_cf_sub)$edf[3]
## [1] 7.419691
draw(f_cf_sub)
## Warning: Removed 910 rows containing non-finite values (stat_contour).

Crossbasis surface looks extremely similar.

Reproducibility

Reproducibility receipt

 
## datetime
Sys.time()
## [1] "2021-08-12 16:39:45 EDT"
## repository
if(requireNamespace('git2r', quietly = TRUE)) {
  git2r::repository()
} else {
  c(
    system2("git", args = c("log", "--name-status", "-1"), stdout = TRUE),
    system2("git", args = c("remote", "-v"), stdout = TRUE)
  )
}
## Local:    revisions /Users/scottericr/Documents/HeliconiaDemography
## Remote:   revisions @ origin (https://github.com/BrunaLab/HeliconiaDemography.git)
## Head:     [5bf30c2] 2021-08-12: improve (technical) explanation of models.  Closes #87
## session info
sessionInfo()
## R version 4.0.2 (2020-06-22)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS  10.16
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats4    parallel  stats     graphics  grDevices datasets  utils    
## [8] methods   base     
## 
## other attached packages:
##  [1] arm_1.11-2        lme4_1.1-27.1     Matrix_1.3-3      MASS_7.3-54      
##  [5] qqplotr_0.0.5     Hmisc_4.5-0       Formula_1.2-4     survival_3.2-11  
##  [9] lattice_0.20-44   readxl_1.3.1      colorspace_2.0-1  rmarkdown_2.7    
## [13] statmod_1.4.36    latex2exp_0.5.0   gratia_0.6.0.9112 broom_0.7.6      
## [17] patchwork_1.1.1   glue_1.4.2        bbmle_1.0.23.1    dlnm_2.4.5       
## [21] mgcv_1.8-36       nlme_3.1-152      lubridate_1.7.10  janitor_2.1.0    
## [25] tsModel_0.6       SPEI_1.7          lmomco_2.3.6      tsibble_1.0.1    
## [29] forcats_0.5.1     stringr_1.4.0     dplyr_1.0.5       purrr_0.3.4      
## [33] readr_1.4.0       tidyr_1.1.3       tibble_3.1.1      ggplot2_3.3.5    
## [37] tidyverse_1.3.1   here_1.0.1        tarchetypes_0.2.0 targets_0.4.2    
## [41] dotenv_1.0.3      conflicted_1.0.4 
## 
## loaded via a namespace (and not attached):
##  [1] backports_1.2.1     igraph_1.2.6        splines_4.0.2      
##  [4] digest_0.6.27       htmltools_0.5.1.1   fansi_0.4.2        
##  [7] magrittr_2.0.1      checkmate_2.0.0     memoise_2.0.0      
## [10] cluster_2.1.2       modelr_0.1.8        bdsmatrix_1.3-4    
## [13] anytime_0.3.9       jpeg_0.1-8.1        rvest_1.0.0        
## [16] haven_2.4.1         xfun_0.22           callr_3.7.0        
## [19] crayon_1.4.1        jsonlite_1.7.2      gtable_0.3.0       
## [22] DEoptimR_1.0-8      abind_1.4-5         scales_1.1.1       
## [25] mvtnorm_1.1-1       DBI_1.1.1           Rcpp_1.0.6         
## [28] isoband_0.2.4       htmlTable_2.1.0     foreign_0.8-81     
## [31] htmlwidgets_1.5.3   httr_1.4.2          RColorBrewer_1.1-2 
## [34] ellipsis_0.3.2      pkgconfig_2.0.3     farver_2.1.0       
## [37] nnet_7.3-16         sass_0.3.1          dbplyr_2.1.1       
## [40] utf8_1.2.1          tidyselect_1.1.1    labeling_0.4.2     
## [43] rlang_0.4.11        munsell_0.5.0       cellranger_1.1.0   
## [46] tools_4.0.2         cachem_1.0.4        cli_2.5.0          
## [49] generics_0.1.0      evaluate_0.14       fastmap_1.1.0      
## [52] yaml_2.2.1          goftest_1.2-2       processx_3.5.2     
## [55] knitr_1.33          fs_1.5.0            robustbase_0.93-7  
## [58] mvnfast_0.2.5.1     xml2_1.3.2          compiler_4.0.2     
## [61] rstudioapi_0.13     png_0.1-7           reprex_2.0.0       
## [64] bslib_0.2.4         stringi_1.6.2       highr_0.9          
## [67] ps_1.6.0            nloptr_1.2.2.2      vctrs_0.3.8        
## [70] pillar_1.6.0        lifecycle_1.0.0     jquerylib_0.1.4    
## [73] data.table_1.14.0   R6_2.5.0            latticeExtra_0.6-29
## [76] renv_0.13.2         gridExtra_2.3       Lmoments_1.3-1     
## [79] codetools_0.2-18    boot_1.3-28         assertthat_0.2.1   
## [82] rprojroot_2.0.2     withr_2.4.2         hms_1.1.0          
## [85] grid_4.0.2          rpart_4.1-15        coda_0.19-4        
## [88] minqa_1.2.4         snakecase_0.11.0    git2r_0.28.0       
## [91] numDeriv_2016.8-1.1 base64enc_0.1-3